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bettyboop8904

  • 3 years ago

Can someone please help me with some integral homework before I shoot the crap out of my calculus book pretty please?! Equation in the forum

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  1. bettyboop8904
    • 3 years ago
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    \[\int\limits_{}^{}\ln (\sqrt[3]{x})\] That is x to the 3 root

  2. mathsmind
    • 3 years ago
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    hi there

  3. bettyboop8904
    • 3 years ago
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    hello = )

  4. jim_thompson5910
    • 3 years ago
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    it might help to think of the cube root of x as x^(1/3)

  5. jim_thompson5910
    • 3 years ago
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    then use the power rule

  6. mathsmind
    • 3 years ago
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    ok do u want me to solve it or should i tell u how to do it

  7. bettyboop8904
    • 3 years ago
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    ok I got as far to as thinking of x^(1/3) lol

  8. jim_thompson5910
    • 3 years ago
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    now use the rule that integral of x^n = (1/(n+1))*x^(n+1)

  9. mathsmind
    • 3 years ago
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    if u solve it i give u medal and if i do so you give me one

  10. bettyboop8904
    • 3 years ago
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    so do u mean put 1/3 in front of the ln of stuff and then put it in front of the entire integral? bc that's what I did and it said it was wrong = (

  11. jim_thompson5910
    • 3 years ago
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    there's no ln involved here

  12. mathsmind
    • 3 years ago
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    u=x^1/3

  13. bettyboop8904
    • 3 years ago
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    ok maybe you should write the whole thing out cuz now you're just confusing me, please, thank you

  14. jim_thompson5910
    • 3 years ago
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    does this rule look familiar |dw:1360297226043:dw|

  15. jim_thompson5910
    • 3 years ago
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    sry the +C is nearly cut off

  16. bettyboop8904
    • 3 years ago
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    no yeah i already know that lol we're in the chapter of integration by parts and there is a ln involved it's in the front of the x^(1/3)

  17. anonymous
    • 3 years ago
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    not to interrupt, but i think the starting point here is \[\frac{1}{3}\int \ln(x)dx\] which you do either by parts or by memory

  18. jim_thompson5910
    • 3 years ago
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    oh my bad, i didn't see the ln at the very beginning just thought it was cube root of x

  19. mathsmind
    • 3 years ago
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    its ok

  20. anonymous
    • 3 years ago
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    since \(\ln(x)\) is a very common function, it might be benificial just to memorize \[\int \ln(x)dx=x\ln(x)-x\] you can check by differentiation

  21. bettyboop8904
    • 3 years ago
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    yes that's what i did. oh damn nvm hahaha i think i get it I keep getting it confused that the derivative of ln is 1/x and we don't know the integral of ln yet so we have to do integration by parts lol

  22. anonymous
    • 3 years ago
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    your answer is therefore \[\frac{1}{3}\left(x\ln(x)-x \right)\]

  23. mathsmind
    • 3 years ago
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    you can use taylor series to integrate this easily

  24. mathsmind
    • 3 years ago
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    but with z=x+1

  25. bettyboop8904
    • 3 years ago
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    you guys were a great help! ty! = )

  26. anonymous
    • 3 years ago
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    i would memorize it just like remembering that \[\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\]so while your fellow classmates are integrating by parts, you just write down the answer

  27. mathsmind
    • 3 years ago
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    i won't recommend that method

  28. mathsmind
    • 3 years ago
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    what about\[\int\limits \ln e^{^{x ^{2}}}dx\]

  29. mathsmind
    • 3 years ago
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    or

  30. mathsmind
    • 3 years ago
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    \[\int\limits \ln(x^x)dx\]

  31. mathsmind
    • 3 years ago
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    or

  32. mathsmind
    • 3 years ago
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    \[\int\limits \ln(x^2+2x+1)dx\]

  33. mathsmind
    • 3 years ago
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    so these are 3 examples that can't be used by just memorizing the specific case

  34. mathsmind
    • 3 years ago
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    so basically use integration by parts like ur class mates

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